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My textbook says
Molarity is dependent on temperature, whereas molality is not.
I'm aware of the definitions of both molarity and molality, but consider this scenario:
A solution of $\ce{NaCl}$ in $\ce{H2O}$ is heated. Eventually, all the water will escape and I will be left with only $\ce{NaCl}$ crystals. At the end, there is no solvent to even measure the concentration of what was once a solution. In this case, how does the argument "molality is independent of temperature" still hold true?
Recall that molarity $c$ is
$$c=\frac{n_\text{solute}}{V_\text{solution}}$$
whereas for molality $b$ is
$$b=\frac{n_\text{solute}}{m_\text{solvent}}$$
While in the extreme case you mentioned, both quantities are not defined because all the solvent is either boiled away (or for heat-sensitive species, the solvent can even decompose under heating), molarity depends on volume, and the volume of the solution depends on temperature due to expansion/contraction.
Example: 5 moles of solute in 1 liter of solution.
The Molarity at the beginning is (5moles ÷ 1Liter) = 5 M.
When the solution is warmed up and expanded by 1% say, to 1.01L, the new Molarity = (5moles ÷ 1.01Liter) = 4.95 M
P.S. Don't over think this question! The amount of content should not change, all you're talking about is expansion of content when the temperature rises. All matter expands when temperature rises so if you're calculating the molarity of a solution, you may get different readings on a warm day compared to a freezing cold day!
Molality doesn't change with temperature...
These two words sound similar but they are not synonyms, even though both of them are used for representing solution concentration. By definition, molarity is the number of moles of solute dissolved per liter of solution. We use capital letter “M” to represent molarity and its formula is M= (# mol SOLUTE)/ (Liters of SOLUTION). Molality is then the number of moles of solute per kilogram of the SOLVENT, NOT solution! We use lower case letter “m” to represent molality and its formula can be represented as: m= (# mole SOLUTE) / (Kilograms of SOLVENT). Most of the time scientists use either molarity or molality to represent solution concentration, but MOLALITY is preferred when the temperature of the solution varies. That is because MOLALITY does not depend on temperature, (Neither number of moles of solute nor mass of solvent will be affected by changes of temperature.) while MOLARITY changes as temperature changes. (Volume of solution in the formula changes as temperature changes, and that is why.)
Okay so no one answered OP properly. Molality(m) is independent of the temperature as long as the temperature change does not actually change the amount of solute. I understand that most resources would not mention this simple fact and expect you to understand it presumptuously. Again, molality(m) is independent of temperature as long as the amount of solvent is not changing.
Example 1: temperature changes --> solution volume changes --> molarity (M) changes --> molality (m) constant
Example 2: temperature changes --> solution volume changes --> amount of solute changes --> molarity (M) changes --> molality (m) changes
See the difference?
Molarity is a temperature-dependent parameter. The volume of a solution increases with an increase in temperature diye to increase in intermolecular spaces and vice versa. Hence, molarity is affected by temperature change. As Molarity (M) is defined as the number of moles of solute (n) divided by the volume (V) of the solution in liters.
